TwiddleLab / Math / Growth: Exponents and Logs
Shrinking: Zero and Negative Powers
What you will learn
- Each floor down divides by the base, so 2⁰ = 1: it is just the next floor after 2¹ = 2.
- A negative exponent means divide: 2⁻ⁿ = 1/2ⁿ. It is never a negative number.
- Small numbers are written with negative powers of 10: 10⁻³ = 0.001.
How the lesson goes
What is 2⁰, zero twos multiplied together?
Calculators have an answer. What is yours? Drag the lever.
Ride the elevator of powers down.
Floor 3 holds 2³ = 8 pieces. Each floor down divides by 2. Ride to floor −2.
Fill the gaps in the ladder.
Tap a chip, then the empty floor. Two chips do not belong anywhere.
Below floor 1, the rhythm keeps going.
2⁰ = 1. It is not "zero twos". It is one floor below 2¹ = 2, and 2 ÷ 2 = 1.
2⁻ⁿ = 1/2ⁿ. The minus says divide n times. 2⁻³ = 1/8.
Any base works the same: 10⁰ = 1, 10⁻² = 1/100.
Put the small powers on the line.
Drag each chip onto the number line where its value is.
Game: elevator rush.
Ride to the floor that holds each target. Fewer moves, more stars.
Build your own ladder of 3s.
Each floor down divides by 3. Put every value on its floor.
AI models learn in tiny steps.
A learning rate sets the size of each step. Set it to 0.001 on the powers of 10 elevator.
Your ladder of 3s, values hidden. Where is 1/9?
Tap the floor that holds 1/9, then Check.
Going down from floor 0 divides by 3 each time: 1, then 1/3, then 1/9. That is two floors down, so 3⁻² = 1/9.
Previous lesson: Exponent Rules by Counting · Next lesson: Half Steps: Roots as Powers · Part of the course: Growth: Exponents and Logs
Lessons are interactive and need JavaScript. Turn it on to play them.
